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That P is intuitive makes P probable?
Maybe there is a huge literature out there about intuition (or rational insight) as a source of justification and knowledge – but I didn’t read any paper on it yet. However, I have a promissory note to deal with questions surrounding this cognitive power. The fact is that every time I read a philosopher accepting or rejecting a certain thesis on the basis that it is intuitive or counter-intuitive, I feel uncomfortable. So, I’ll try to explain why that is so. At the same time, I would like to know if the reader of this post feels completely assured that intuition is a good source of justification and knowledge (you can feel comfortable to indicate papers dealing with this question).
Doubts surrounding intuition can arise when one is in the context of philosophical discourse. In such context, it is usual to present philosophical analyzes by means of propositions with the form:
x is A if, and only if, x is B,
or:
x is A only if x is B
where ‘A’ and ‘B‘ are predicates standing for relations and properties (or sets of relations and/or properties). Generally, it is said that beliefs in such propositions are justified a priori – by means of reasoning from justified premises, or by means of understanding the meanings of ‘A’ and ‘B’, or then by means of rational intuition. It seems it is not as clear how such beliefs are justified by intuition as it is when they are justified by reasoning and linguistic understanding – what is a rational intuition? What epistemic properties it has?
Nevertheless, philosophers in general make use of intuition to refute and endorse propositions with that form. The theoretical procedure of endorsing a proposition by means of intuition can be represented by the following argument-type:
(i) It is intuitive that x is A only if x is B
(ii) Therefore, x is A only if x is B
This argument-type is instantiated by, for example:
(i’) It is intuitive that, if S knows that P, then S has some degree of certainty with respect to P
(ii’) therefore, if S knows that P, then S has some degree of certainty with respect to P
In a similar way, there is a theoretical procedure in which one refutes a proposition by means of intuition that can be represented by the following argument-type:
(iii) It is counter-intuitive that x is A when x is B
(iv) Therefore, x is not A when x is B
This argument-type is instantiated by, for example:
(iii’) It is counter-intuitive that S has knowledge when S has a justified belief which is accidentally true
(iv’) Therefore, S does not have knowledge when S has a justified belief which is accidentally true
What kind of argument is that authorizing the passage from (i) to (ii) and from (iii) to (iv)? Clearly, the argument is not a valid one: it is possible for the conclusion to be false while the premise is true. It can perfectly be the case that P is intuitive and false, as it can perfectly be the case that P is counter-intuitive and true.
But there is another option for taking these arguments as good ones (that is, not ill-formed): they are inductively strong (or cogent as Feldman calls it in Reason & Argument). In that case, the thesis is as follows:
(IN) If it is intuitive that P, then P is probably the case
And, if (IN) is the case, the following epistemic norm can be derived:
(ENI) When P is intuitive to S, S is epistemically insured in believing that P
This epistemic norm does not require S to know/justifiably believe that (IN) is the case – intuition can play its justificatory role even if neither (IN) nor (ENI) are actually accessed by S. The worry about the epistemic status of (IN) is part of the epistemologist job, however, which wants to justify the epistemic norm (ENI). Now, my question is: how can the epistemologist justify (IN)? What reasons we have to believe it is true?
Nita 8:16 pm on October 20, 2011 Permalink |
Great post! As it happened before, my spontaneous reactions and comments are confined to a limited understanding of this problem from a moral, epistemological standpoint. As I told you before, the very intriguing thing when dealing with intuition and intuitionism in Rawl’s moral philosophy is that it makes us wonder whether one can at once refuse moral intuitionism (understood as rational intuitionism or moral Platonism as spoused by Clarke, Price, Leibniz, Wolff, Sidgwick and Moore) and embrace constructivism (itself akin to a version of mathematical intuionism). I tend to disagree with most analytic realist readings of this issue, for instance, when Audi regards Kant’s ethics as intuitionist (Mind 2001 article, attached as PDF). It seems that intuitionism is inevitably reducible to moral realism, as one thinks of an immediate take on moral issues, say, that “torture is morally wrong” (not to say that “punching babies is morally wrong” and this kind of self-evident “intuitions” for US students). Precisely because I do believe that both torture and punching babies are morally wrong but these beliefs are not immediately given I tend to take distance from most Anglo-American moral realists, esp. whenever they seem to betray some form of conservative, theological realism (as Professor Plantinga just showed us right here at PUCRS). I am a very liberal animal, so I am quite respectful of these gentlemen’s views but I am not convinced and must be honest to admit that I still keep guard against cryptofundamentalist agendas. Kant seems to be a good watershed because the way one reads the Kantian critique of Platonic, Cartesian intuitionism (which includes theological and metaphysical presuppositions about nature and reality overall) could help us make sense of our own contemporary understanding of these problems. So I am assuming that when you talk about “rational intuition” you mean what Kant called “a priori” or somewhat related to pure reason. For instance, when Kant thinks of space and time as forms of intuition, in that they depend on the “subjective constitution of the mind.” And yet Kant’s conception of intuition accounts also for our everyday usage of the term, say, in perception, when we see that the sky is blue or hear the noise of a car approaching. For Kant, intuition, in this latter sense, is always sensible intuition, as our immediate representation of things or phenomenal beings always refers us to their being in space and time and available to our sense perception without recourse to inference or reason. Moreover, there is no such thing as an intellectual intuition (a Hegelian metaphysical invention of sorts!) For Kant, intuitions are thus objective representations and as such we almost take for granted that the board in our classroom is green, that the door is open or closed etc –most of our daily experiences in dealing with things and nature, in contingent, synthetic a posteriori fashion. The funny thing is that, according to Kant, we can also have pure intutitions, precisely like the non-empirical, immediate representations of space and of time. It seems that in philosophy of math this has been a big, controversial problem whenever we say that “1 + 1 = 2″ stands for an example of intuition. For as we all know, Kant thought that this would rather be an example of a synthetic a priori judgment. That is why intuitionism and constructivism stem from the Kantian take on pure intuition, in a rather different account from traditional, Platonic intuitionism and formalism. Now, when you raise the question “What reasons do we have to believe (anything intuitive) is true?” –a damn good question by the way– it seems that, in moral epistemology, it all depends on what context for giving reasons is meant, say, for the right action or in a metaphysical sense (such as the Platonic realm of Forms or any theory of the Good that claims to be prior to social reality). I understand that you probably don’t want to place your inquiry within social epistemology but since analytic philosophy is committed to holism or avoiding dualisms I thought you might want to respond to this provocation!
nythamar 10:28 am on October 21, 2011 Permalink |
Check this out:
http://philosophy.ucdavis.edu/mattey/kant/INTUIT.HTM
Kant Lexicon
Intuition (Anschauung)
A320-B377: Intuition is a mode of cognition, which “relates immediately to the object, and is single.”
A19/B33: “In whatever manner and by whatever means a mode of cognition may relate to objects, intuition is that through which it is in immediate relation to them . . . But intuition takes place only in so far as the object is given to us.”
To say that intuition relates immediately to the object means that it represents the object without bringing it under a general concept.
Intuitions represent single objects, particulars, rather than groups of objects. It is general concepts which represent many single things under one heading.
Kant held that human intuition is sensible. That is, the objects of intuition are “given” to the mind, which is “affected” by them. Sensibility is the faculty of the mind which is affected by objects.
“Our mode of intuition is dependent upon the existence of the object, and is threfore possible only if the subjects’ faculty of representation is affected by that object. . . . It is derivative (intuitus derivativus), not original (intuitus originarius) , and, therefore not an intellectual intuition” (B72).
It is conceivable that some minds have an intuition that is intellectual. It would represent objects immediately without being affected by them. Kant held that we do not know whether this is possible, since we do not know how it could occur. The only clue we have is that if there is a God or primordial being, it would have to have original intuition. The reason is that such a being’s cognition must be intuitive, but it could not intuit anything sensibly, as this would be a limitation. (B71, cf. B138)
nythamar 10:42 am on October 21, 2011 Permalink |
Another helpful, thought-provoking link from a doctoral student, Sharon Berry, from Harvard:
http://www.people.fas.harvard.edu/~seberry/evolution/#_ftnref1
Evolution, Induction and Rational Intuition
Intro
Rational intuition: There are a number of things which can be called rational intuition[1]. Here I simply mean the fairly immediate/spontaneous/off the cuff inclination to say that a certain sentence is true without, say, looking a proof or learning this by testimony. So, for example when you immediately accept or feel that you can directly ‘see’ the truth of a statement or when you go through one example (or fewer) and then are inclined to think, without proof, that all other examples will work out the same way these would all be examples of rational intuition in the sense that I have in mind.
We take rational intuition to very frequently lead us to true conclusions though it is not infallible.
There is probably an evolutionary explanation for how such intuitions can so frequently get things right. In this section I will consider some philosophical problems for such an account.
One note before we get started though:
Often we have rational intuitions about propositions which can be proved from accepted axioms so one might think that all such intuitions are a matter of subconsciously working out a proof. This doesn’t seem likely for a number of reasons. First off we can have apparently quite similar intuitions about statements like the axiom of choice which can’t be proved from accepted axioms. Secondly accepted axioms often seem intuitive themselves in a very similar way as propositions which can be proved in terms of them – rather than feeling somehow especially trivial. This is, of course, consistent with the idea that the mechanism which produces rational intuitions effectively tries to prove the statement in question from our accepted axioms and gives us the feeling that such statements must be true when such a subconscious proof can be given (in the case of the axioms these proofs will just be proofs of one line). However, this hypothesis that cultural acceptance of certain axioms precedes mathematical intuition seems very unlikely. It is surely more plausible to think that intuition precedes axiom choice: that a number of related statements all seem intuitively likely and we choose some of them as axioms in such a way as to entail as many of the others as possible.
Thus for these two reasons the fact that many things which are intuitive can be proved should not be taken to mean that mathematical intuition is a matter of unconsciously grasping a proof (though, of course one thing we can have a mathematical intuition about is the claim that something can be proved).
Impossibility argument
If scientific induction is completely unreliable in the realm of necessary truths then it is surprising that evolution would lead people to accept true axioms and inference procedures.
For, if there is a humanly detectable kind of inferential procedure such that the fact that a number of instances of a procedure of this kind don’t lead from truth to falsehood makes it likely that the inference procedure is infact truth preserving, then we will get both a justification for induction about math+logic and an evolutionary explanation for how we could evolve a faculty of rational intuition. Otherwise we get neither.
I think that we should accept both the evolutionary account of rational intuition and the idea that in some cases induction can justify us in believing necessary logico-mathematical truths.
A strong Platonist might object that what we evolve is a faculty that literally detects the forms. But if you don’t accept such causal powers then it is hard to see what the sub-personal mechanisms evolved could do to get reliability that conscious induction can’t.
Here are a few points to soften the blow of accepting that we can have mathematical knowledge by induction
calculator example
could learn that everyone in group A qualifies for insurance plan 5 inductively
obviously some mathematical predicates aren’t very inductable but neither are some empirical ones… all we need is that there is some subset of mathematical claims which humans can distinguish which are inductible
in some cases we are inclined to use knowledge to mean possession of a canonical proof as distinct from reliable belief: so if you are inclined to say that you cant *know* mathematical truths by scientific induction in the special sense which is normally relevant to mathematical statements this does not entail that induction can’t lead you to reliable true beliefs.
Specific problems for coming up with an evolutionary story about rationality:
What is it for a creature to be able to infer from ‘P v Q and ~Q’ to ‘P’ – need to associate these two logically equivalent propositions with different mental states such that some creature could be evolutionarally disadvantaged by not connecting these states.
[This is a variant of the problem of logical omniscience: it is tempting to think of a creature’s mental states in terms of the set of possible worlds which are actual for all we know.]
In order to get an evolutionary grip we would need to have separate behavioral states associated with the two necessary beliefs, which there could then be some evolutionary value to evading.
Suppose:
Mice can detect vixen urine.
Mice can detect foxes visually, and go into fox evasion procedure when they do.
If a mouse smells the vixen urine but doesn’t start the fox evasion procedures we might say that it knows that there is a fox but not that that there is a vixen.
In this way there could be selection for either
a) mice with brains that automatically connected these two states
b) mice with brains that would end up connecting these states if they were frequently enough activated next to each other (i.e. brains that treated these predicates as inductible)
In this way, if we think that it makes sense to attribute logical abilities to pre-lingusitic animals we can make sense of evolution giving them these linguistic abilities.
On the other hand if you don’t think it makes sense to attribute logico-mathematical abilities to animals then the story is even easier to tell once language is in place
Suppose:
People can recognize vixens by seeing them or by hearing others say vixen
People can recognize foxes by seeing them or by hearing others say fox, and they have fox hunting/evasion procedures
There would be survival value to going to get your fox spear directly when someone says vixen rather than waiting for someone to say that is a fox too, or waiting for it to come into sight.
Since language chances so quickly it’s unlikely that there would be benefit in making a brain that ‘automatically’ believes that vixens are foxes.
But there would be a benefit to build a brain which is likely to connect these kinds of states (one that treats these states as inductive).
We would be evolved to have a sense of the ‘right’ kinds of inferential procedures to accept as universally true after relatively few confirmatory experiences, just as we are evolved to have a sense of the ‘right’ kind of generalizations about the empirical world (pots that look like this will crack when fired, treating bees like this will make them aggressive) to believe on the basis of very limited experience.
In this way our intuition that the pigeon-hole principle is true is like our intuition that you can’t cut a banana with a telephone wire (we are evolved to quickly, subconsciously, make certain kinds of generalizations on the basis of very limited observation)
The only difference is that in the latter case we can form certain kinds of pictures of mere physical impossibilities but not metaphysical/mathematical impossibilities.
But these canonical methods of picturing are just formed by a) evolution and b) custom in such a way that everything which is actual/physically possible turns out to be picturable. But there are no further constraints: whether we say that a given description of a physically possible state of affairs is or is not metaphysically possible is just a matter of chance and convention.
nythamar 10:23 pm on October 21, 2011 Permalink |
Once again, let me try to make sense of my take on rational intuition:
The major problem with moral intuitionism, as Rawls correctly put it, is its taking for granted so-called prima facie moral convictions or beliefs as something self-evident. A moral intuition comes down to believing something irreducibly given, as it were a brute fact, the plain truth or the real thing. A Cartesian genius, G-d or Coca-Cola, for that matter, seem to be all likely to be mistaken for intuitive beliefs and the object of warranted belief. Once again, we must reexamine the grammar of belief and the ontological commitments involved in such metaethical assumptions. In Kantian terms, we must distiguish opining, knowing, and believing (KrV A820/B 848 Canon of Pure Reason section 3). According to our coherentist, Rawlsian-like reading of Kant’s epistemology, the only way to know something is by appealing to beliefs and that which is regarded as being true is that which is consistent with our overall network of beliefs. In Rawlsian-Kantian terms that means that there are no foundational propositions leading to some basic beliefs in order to act morally (once again, think of giving reasons to act morally as a procedural device, say, like the categorical imperative).
So that accounts for traditional accounts of cognition as “justified true belief” in a much weaker sense (hence, shifting away from robust cognitivism and moral realism) but also for the semantic, ontological implications in a post-Gettier account of lucky guesses, moral luck, luck egalitarianism, and so forth. For Kant the bottom line is that we must make a distinction between theoretical and practical uses of reason, and this what lends to confusion when most believers take for granted that because it seems consistent to hold moral beliefs and believe in G-d that Kant seems to be making a case for a theistic view of moral realism. Kant’s antirealism can be thus placed somewhere between Platonic, moral realism and Humean noncognitivism, just like R.M. Hare and J. Rawls have convincingly argued.
Luis Rosa 7:44 pm on October 22, 2011 Permalink |
Hello Nythamar! You brought lots of points since the first comment, but I think it is noteworthy that the kantian take on intuition is very different from the contemporary epistemologist’s take on it. they are not talking about the same thing. kant is talking about intuition of particulars, objects. the hangout on intuition from the contemporary epistemology point of view is concerned with another kind of object – propositions and beliefs. it seems the intuitions of particulars via sensation is not the same thing as intuition as a source of justification for beliefs in propositions. It is one thing to have an intuition of an object, and another to have an intuition that…, where the ‘…’ is completed by a proposition or declarative sentence. On the same moods, I would say the quotation from Sharon Berry goes straight to the epistemological point that is in question here – so that is the meaning of ‘intuition’ we’re using.
Now, turning to the epistemological status of beliefs gattered via intuition: there is the possibility for one to believe that (IN) is the case on the basis that, most of the times we have an intuition that P is the case, P is the case. That would be an inductive reasoning giving support to the reliability of intuition – and intuition would be a derivative source of justification. It is believed to be reliable on the basis of reasoning and any other source of justification (examples can be given with the use of perception, testimony and memory confirming the proposition that was the object of intuition and believed to be the case). It follows from this hypothesis that intuition is not a basic source of justification – and it seems to me this result would be unwelcome for some classic apriorists (I owe this point to Alexandre Junges, which answered during a lunch how he would answer the question about the reliability of intuition).